Some patients taking anti-HIV drugs as part of highly active antiretroviral therapy (HAART) do not show any HIV in the blood; however, some HIV will remain hidden in the body and, if the drugs are stopped, will return to the blood. The purpose of this study is to determine if short periods of stopping HAART increase the activity of CD8 and CD4 cells (cells of the immune system that fight infection), if repeated stopping of these drugs for longer periods of time and restarting them will increase effectiveness of HAART, and if the increased immune system activity as a result of stopping treatment leads to lower levels of HIV over time.